This paper presents a new method of grouping edges in order to recognize objects. This grouping method succeeds on images of both two- and three-dimensional objects. So that the recognition system can consider first the collections of edges most likely to lead to the correct recognition of objects, we order groups of edges based on the likelihood that a single object produced them. The grouping module estimates this likelihood using the distance that separates edges and their relative orientation. This ordering greatly reduces the amount of computation required to locate objects. Surprisingly, in some circumstances grouping can also improve the accuracy of a recognition system that handles libraries of two-dimensional, polygonal objects. Second, we show comparable performance of the grouping system on images of two- and three-dimensional objects. This provides evidence that the grouping system could produce significant improvements in the performance of a three-dimensional recognition system.